Solve for $k$, $ \dfrac{9}{8k} = \dfrac{4}{20k} - \dfrac{5k + 3}{4k} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $8k$ $20k$ and $4k$ The common denominator is $40k$ To get $40k$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ \dfrac{9}{8k} \times \dfrac{5}{5} = \dfrac{45}{40k} $ To get $40k$ in the denominator of the second term, multiply it by $\frac{2}{2}$ $ \dfrac{4}{20k} \times \dfrac{2}{2} = \dfrac{8}{40k} $ To get $40k$ in the denominator of the third term, multiply it by $\frac{10}{10}$ $ -\dfrac{5k + 3}{4k} \times \dfrac{10}{10} = -\dfrac{50k + 30}{40k} $ This give us: $ \dfrac{45}{40k} = \dfrac{8}{40k} - \dfrac{50k + 30}{40k} $ If we multiply both sides of the equation by $40k$ , we get: $ 45 = 8 - 50k - 30$ $ 45 = -50k - 22$ $ 67 = -50k $ $ k = -\dfrac{67}{50}$